Deck 24: Gausss Law

Question 1

A charge (uniform linear density = 9.0 nC/m) is distributed along the x axis from x = 0 to x = 3.0 m. Determine the magnitude of the electric field at a point on the x axis with x = 4.0 m.

A) 81 N/C
B) 74 N/C
C) 61 N/C
D) 88 N/C
E) 20 N/C

Answer 1

61 N/C

Question 2

A uniformly charged rod (length = 2.0 m, charge per unit length = 3.0 nC/m) is bent to form a semicircle. What is the magnitude of the electric field at the center of the circle?

A) 64 N/C
B) 133 N/C
C) 48 N/C
D) 85 N/C
E) 34 N/C

Answer 2

85 N/C

Question 3

A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m. Which of the following integrals is correct for the y component of the electric field at y = 4 m on the y axis?

A)

B)

C)

D)

E) none of these

Answer 3

Question 4

A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m. Which of the following integrals is correct for the x component of the electric field at y = 2 m on the y axis?

A)

B)

C)

D)

E) none of these

Question 5

A charge of 25 nC is uniformly distributed along a circular arc (radius = 2.0 m) that is subtended by a 90-degree angle. What is the magnitude of the electric field at the center of the circle along which the arc lies?

A) 81 N/C
B) 61 N/C
C) 71 N/C
D) 51 N/C
E) 25 N/C

Question 6

Two charges of 15 pC and −40 pC are inside a cube with sides that are of 0.40-m length. Determine the net electric flux through the surface of the cube.

A) +2.8 N ⋅ m²/C
B) −1.1 N ⋅ m²/C
C) +1.1 N ⋅ m²/C
D) −2.8 N ⋅ m²/C
E) −0.47 N ⋅ m²/C

Question 7

A rod (length = 2.0 m) is uniformly charged and has a total charge of 40 nC. What is the magnitude of the electric field at a point which lies along the axis of the rod and is 3.0 m from the center of the rod?

A) 40 N/C
B) 45 N/C
C) 24 N/C
D) 90 N/C
E) 36 N/C

Question 8

A 24-nC charge is distributed uniformly along the x axis from x = 2 m to x = 6 m. Which of the following integrals is correct for the magnitude (in N/C) of the electric field at x = +8 m on the x axis?

A)

B)

C)

D)

E) none of these

Question 9

Charge of uniform density 4.0 nC/m is distributed along the x axis from x = −2.0 m to x = +3.0 m. What is the magnitude of the electric field at the point x = +5.0 m on the x axis?

A) 16 N/C
B) 13 N/C
C) 19 N/C
D) 26 N/C
E) 5.0 N/C

Question 10

A charge of 80 nC is uniformly distributed along the x axis from x = 0 to x = 2.0 m. Determine the magnitude of the electric field at a point on the x axis with x = 8.0 m.

A) 30 N/C
B) 15 N/C
C) 48 N/C
D) 90 N/C
E) 60 N/C

Question 11

A uniform linear charge density of 4.0 nC/m is distributed along the entire x axis. Consider a spherical (radius = 5.0 cm) surface centered on the origin. Determine the electric flux through this surface.

A) 68 N ⋅ m²/C
B) 62 N ⋅ m²/C
C) 45 N ⋅ m²/C
D) 79 N ⋅ m²/C
E) 23 N ⋅ m²/C

Question 12

A charge of 50 nC is uniformly distributed along the y axis from y = 3.0 m to y = 5.0 m. What is the magnitude of the electric field at the origin?

A) 18 N/C
B) 50 N/C
C) 30 N/C
D) 15 N/C
E) 90 N/C

Question 13

A uniform linear charge of 3.0 nC/m is distributed along the y axis from y = −3 m to y = 2m. Which of the following integrals is correct for the magnitude of the electric field at y = 4 m on the y axis?

A)

B)

C)

D)

E) none of these

Question 14

A 16-nC charge is distributed uniformly along the x axis from x = 0 to x = 4 m. Which of the following integrals is correct for the magnitude (in N/C) of the electric field at x = +10 m on the x axis?

A)

B)

C)

D)

E) none of these

Question 15

A uniform linear charge density of 7.0 nC/m is distributed along the y axis from y = 2 m to y = 5 m. Which of the following integrals is correct for the magnitude (in N/C) of the electric field at y = 0 on the y axis?

A)

B)

C)

D)

E) none of these

Question 16

A uniformly charged rod (length = 2.0 m, charge per unit length = 5.0 nC/m) is bent to form one quadrant of a circle. What is the magnitude of the electric field at the center of the circle?

A) 62 N/C
B) 56 N/C
C) 50 N/C
D) 44 N/C
E) 25 N/C

Question 17

The total electric flux through a closed cylindrical (length = 1.2 m, diameter = 0.20 m) surface is equal to −5.0 N ⋅ m²/C. Determine the net charge within the cylinder.

A) −62 pC
B) −53 pC
C) −44 pC
D) −71 pC
E) −16 pC

Question 18

Charges q and Q are placed on the x axis at x = 0 and x = 2.0 m, respectively. If q = −40 pC and Q = +30 pC, determine the net flux through a spherical surface (radius = 1.0 m) centered on the origin.

A) −9.6 N ⋅ m²/C
B) −6.8 N ⋅ m²/C
C) −8.5 N ⋅ m²/C
D) −4.5 N ⋅ m²/C
E) −1.1 N ⋅ m²/C

Question 19

A uniform charge density of 500 nC/m³ is distributed throughout a spherical volume (radius = 16 cm). Consider a cubical (4.0 cm along the edge) surface completely inside the sphere. Determine the electric flux through this surface.

A) 7.1 N ⋅ m²/C
B) 3.6 N ⋅ m²/C
C) 12 N ⋅ m²/C
D) 19 N ⋅ m²/C
E) 970 N ⋅ m²/C

Question 20

A 12-nC charge is distributed uniformly along the y axis from y = 0 to y = 4 m. Which of the following integrals is correct for the x component of the electric field at x = 2 m on the x axis?

A)

B)

C)

D)

E) none of these

Question 21

A point charge +Q is located on the x axis at x = a, and a second point charge −Q is located on the x axis at x = −a. A Gaussian surface with radius r = 2a is centered at the origin. The flux through this Gaussian surface is

A) zero because the negative flux over one hemisphere is equal to the positive flux over the other.
B) greater than zero.
C) zero because at every point on the surface the electric field has no component perpendicular to the surface.
D) zero because the electric field is zero at every point on the surface.
E) none of the above.

Question 22

Charge of uniform surface density (0.20 nC/m²) is distributed over the entire xy plane. Determine the magnitude of the electric field at any point having z = 2.0 m.

A) 17 N/C
B) 11 N/C
C) 23 N/C
D) 28 N/C
E) 40 N/C

Question 23

A hemispherical surface (half of a spherical surface) of radius R is located in a uniform electric field of magnitude E that is parallel to the axis of the hemisphere. What is the magnitude of the electric flux through the hemisphere surface?

A) πR²E
B) 4πR²E/3
C) 2πR²E/3
D) πR²E/2
E) πR²E/3

Question 24

Charge of a uniform density (8.0 nC/m²) is distributed over the entire xy plane. A charge of uniform density (3.0 nC/m²) is distributed over the parallel plane defined by z = 2.0 m. Determine the magnitude of the electric field for any point with z = 3.0 m.

A) 0.79 kN/C
B) 0.17 kN/C
C) 0.62 kN/C
D) 0.34 kN/C
E) 0.28 kN/C

Question 25

A long cylindrical shell (radius = 2.0 cm) has a charge uniformly distributed on its surface. If the magnitude of the electric field at a point 8.0 cm radially outward from the axis of the shell is 85 N/C, how much charge is distributed on a 2.0-m length of the charged cylindrical surface?

A) 0.38 nC
B) 0.76 nC
C) 0.19 nC
D) 0.57 nC
E) 0.98 nC

Question 26

Each 2.0-m length of a long cylinder (radius = 4.0 mm) has a charge of 4.0 nC distributed uniformly throughout its volume. What is the magnitude of the electric field at a point 5.0 mm from the axis of the cylinder?

A) 9.9 kN/C
B) 8.1 kN/C
C) 9.0 kN/C
D) 7.2 kN/C
E) 18 kN/C

Question 27

A long nonconducting cylinder (radius = 12 cm) has a charge of uniform density (5.0 nC/m³) distributed throughout its column. Determine the magnitude of the electric field 5.0 cm from the axis of the cylinder.

A) 25 N/C
B) 20 N/C
C) 14 N/C
D) 31 N/C
E) 34 N/C

Question 28

A long cylinder (radius = 3.0 cm) is filled with a nonconducting material which carries a uniform charge density of 1.3 μC/m³. Determine the electric flux through a spherical surface (radius = 2.0 cm) which has a point on the axis of the cylinder as its center.

A) 5.7 N ⋅ m²/C
B) 4.9 N ⋅ m²/C
C) 6.4 N ⋅ m²/C
D) 7.2 N ⋅ m²/C
E) 15 N ⋅ m²/C

Question 29

A charge of 0.80 nC is placed at the center of a cube that measures 4.0 m along each edge. What is the electric flux through one face of the cube?

A) 90 N ⋅ m²/C
B) 15 N ⋅ m²/C
C) 45 N ⋅ m²/C
D) 23 N ⋅ m²/C
E) 64 N ⋅ m²/C

Question 30

Two infinite parallel surfaces carry uniform charge densities of 0.20 nC/m² and −0.60 nC/m². What is the magnitude of the electric field at a point between the two surfaces?

A) 34 N/C
B) 23 N/C
C) 45 N/C
D) 17 N/C
E) 90 N/C

Question 31

A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m. What is the x component of the electric field at y = 2 m on the y axis?

A) −5.0 N/C
B) −4.0 N/C
C) −5.7 N/C
D) −6.2 N/C
E) −9.0 N/C

Question 32

A charge of uniform volume density (40 nC/m³) fills a cube with 8.0-cm edges. What is the total electric flux through the surface of this cube?

A) 2.9 N ⋅ m²/C
B) 2.0 N ⋅ m²/C
C) 2.6 N ⋅ m²/C
D) 2.3 N ⋅ m²/C
E) 1.8 N ⋅ m²/C

Question 33

Charge of uniform density (0.30 nC/m²) is distributed over the xy plane, and charge of uniform density (−0.40 nC/m²) is distributed over the yz plane. What is the magnitude of the resulting electric field at any point not in either of the two charged planes?

A) 40 N/C
B) 34 N/C
C) 28 N/C
D) 46 N/C
E) 6.0 N/C

Question 34

A long nonconducting cylinder (radius = 12 cm) has a charge of uniform density (5.0 nC/m³) distributed throughout its volume. Determine the magnitude of the electric field 15 cm from the axis of the cylinder.

A) 20 N/C
B) 27 N/C
C) 16 N/C
D) 12 N/C
E) 54 N/C

Question 35

Charge of a uniform density (8.0 nC/m²) is distributed over the entire xy plane. A charge of uniform density (5.0 nC/m²) is distributed over the parallel plane defined by z = 2.0 m. Determine the magnitude of the electric field for any point with z = 1.0 m.

A) 0.45 kN/C
B) 0.17 kN/C
C) 0.28 kN/C
D) 0.73 kN/C
E) 0.62 kN/C

Question 36

Charge of uniform surface density (4.0 nC/m²) is distributed on a spherical surface (radius = 2.0 cm). What is the total electric flux through a concentric spherical surface with a radius of 4.0 cm?

A) 2.8 N ⋅ m²/C
B) 1.7 N ⋅ m²/C
C) 2.3 N ⋅ m²/C
D) 4.0 N ⋅ m²/C
E) 9.1 N ⋅ m²/C

Question 37

The xy plane is "painted" with a uniform surface charge density which is equal to 40 nC/m². Consider a spherical surface with a 4.0-cm radius that has a point in the xy plane as its center. What is the electric flux through that part of the spherical surface for which z > 0?

A) 14 N ⋅ m²/C
B) 11 N ⋅ m²/C
C) 17 N ⋅ m²/C
D) 20 N ⋅ m²/C
E) 23 N ⋅ m²/C

Question 38

A long nonconducting cylinder (radius = 6.0 mm) has a nonuniform volume charge density given by αr², where α = 6.2 mC/m⁵ and r is the distance from the axis of the cylinder. What is the magnitude of the electric field at a point 2.0 mm from the axis?

A) 1.4 N/C
B) 1.6 N/C
C) 1.8 N/C
D) 2.0 N/C
E) 5.4 N/C

Question 39

Two infinite, uniformly charged, flat surfaces are mutually perpendicular. One of the sheets has a charge density of +60 pC/m², and the other carries a charge density of −80 pC/m². What is the magnitude of the electric field at any point not on either surface?

A) 1.1 N/C
B) 5.6 N/C
C) 7.9 N/C
D) 3.8 N/C
E) 4.0 N/C

Question 40

The electric field in the region of space shown is given by N/C where y is in m. What is the magnitude of the electric flux through the top face of the cube shown?

A) 90 N ⋅ m²/C
B) 6.0 N ⋅ m²/C
C) 54 N ⋅ m²/C
D) 12 N ⋅ m²/C
E) 126 N ⋅ m²/C

Question 41

Three originally uncharged infinite parallel planes are arranged as shown. Then the upper plate has surface charge density σ placed on it while the lower plate receives surface charge density −σ. The net charge induced on the center plate is

A) 0.
B) −σ/2.
C) +σ/2.
D) −σ.
E) +σ.

Question 42

Two concentric imaginary spherical surfaces of radius R and 2R respectively surround a positive point charge Q located at the center of the surfaces. When compared to the electric flux Φ₁ through the surface of radius R, the electric flux Φ₂ through the surface of radius 2R is

A)
.
B)
.
C) Φ₂ = Φ₁.
D) Φ₂ = 2Φ₁.
E) Φ₂ = 4Φ₁.

Question 43

A point charge (5.0 pC) is located at the center of a spherical surface (radius = 2.0 cm), and a charge of 3.0 pC is spread uniformly upon this surface. Determine the magnitude of the electric field 1.0 cm from the point charge.

A) 0.72 kN/C
B) 0.45 kN/C
C) 0.63 kN/C
D) 0.90 kN/C
E) 0.18 kN/C

Question 44

The electric flux through the two adjacent spherical surfaces shown below is known to be the same. It is also known that there is no charge inside either spherical surface. We can conclude that

A) there is no electric field present in this region of space.
B) there is a constant E field present in this region of space.
C) the electric flux has a constant value of zero.
D) any of the above may be correct.
E) only (a) and (b) above may be correct.

Question 45

A charge of 8.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm), and a second charge of −3.0 pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm). Determine the magnitude of the electric field 5.0 cm from the center of the two surfaces.

A) 14 N/C
B) 11 N/C
C) 22 N/C
D) 18 N/C
E) 40 N/C

Question 46

Which one of the following is not an expression for electric charge?

A)

B)

C)

D)

E)

Question 47

A 5.0-nC point charge is embedded at the center of a nonconducting sphere (radius = 2.0 cm) which has a charge of −8.0 nC distributed uniformly throughout its volume. What is the magnitude of the electric field at a point that is 1.0 cm from the center of the sphere?

A) 1.8 × 10⁵ N/C
B) 9.0 × 10⁴ N/C
C) 3.6 × 10⁵ N/C
D) 2.7 × 10⁵ N/C
E) 7.2 × 10⁵ N/C

Question 48

Charge of uniform density (40 pC/m²) is distributed on a spherical surface (radius = 1.0 cm), and a second concentric spherical surface (radius = 3.0 cm) carries a uniform charge density of 60 pC/m². What is the magnitude of the electric field at a point 4.0 cm from the center of the two surfaces?

A) 3.8 N/C
B) 4.1 N/C
C) 3.5 N/C
D) 3.2 N/C
E) 0.28 N/C

Question 49

Two concentric imaginary spherical surfaces of radius R and 2R respectively surround a positive point charge −Q located at the center of the surfaces. When compared to the electric flux Φ₁ through the surface of radius R, the electric flux Φ₂ through the surface of radius 2R is

A)
.
B)
.
C) Φ₂ = Φ₁.
D) Φ₂ = 2Φ₁.
E) Φ₂ = 4Φ₁.

Question 50

When a cube is inscribed in a sphere of radius r, the length L of a side of the cube is . If a positive point charge Q is placed at the center of the spherical surface, the ratio of the electric flux Φ_sphere at the spherical surface to the flux Φ_cube at the surface of the cube is

A)
.
B)
.
C) 1.
D)
.
E)
.

Question 51

A charge of 5.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm), and a second charge of −2.0 pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm). Determine the magnitude of the electric field 3.0 cm from the center of the two surfaces.

A) 30 N/C
B) 50 N/C
C) 40 N/C
D) 20 N/C
E) 70 N/C

Question 52

Charge of uniform density (80 nC/m³) is distributed throughout a hollow cylindrical region formed by two coaxial cylindrical surfaces of radii 1.0 mm and 3.0 mm. Determine the magnitude of the electric field at a point which is 2.0 mm from the symmetry axis.

A) 7.9 N/C
B) 9.0 N/C
C) 5.9 N/C
D) 6.8 N/C
E) 18 N/C

Question 53

Which one of the following cannot be a statement of Gauss's Law for some physical situation?

A) 4πr²ε₀E = Q.
B) 2πrLε₀E = Q.
C)
.
D)
.
E)
.

Question 54

Charge of uniform density (80 nC/m³) is distributed throughout a hollow cylindrical region formed by two coaxial cylindrical surfaces of radii 1.0 mm and 3.0 mm. Determine the magnitude of the electric field at a point which is 4.0 mm from the symmetry axis.

A) 7.9 N/C
B) 10 N/C
C) 9.0 N/C
D) 8.9 N/C
E) 17 N/C

Question 55

Charge of uniform density (20 nC/m²) is distributed over a cylindrical surface (radius = 1.0 cm), and a second coaxial surface (radius = 3.0 cm) carries a uniform charge density of −12 nC/m². Determine the magnitude of the electric field at a point 2.0 cm from the symmetry axis of the two surfaces.

A) 2.3 kN/C
B) 1.1 kN/C
C) 1.7 kN/C
D) 3.4 kN/C
E) 4.5 kN/C

Question 56

Charge of uniform density (20 nC/m²) is distributed over a cylindrical surface (radius = 1.0 cm), and a second coaxial surface (radius = 3.0 cm) carries a uniform charge density of −12 nC/m². Determine the magnitude of the electric field at a point 4.0 cm from the symmetry axis of the two surfaces.

A) 0.45 kN/C
B) 1.0 kN/C
C) 0.73 kN/C
D) 0.56 kN/C
E) 2.3 kN/C

Question 57

Charge of uniform density (40 pC/m²) is distributed on a spherical surface (radius = 1.0 cm), and a second concentric spherical surface (radius = 3.0 cm) carries a uniform charge density of 60 pC/m². What is the magnitude of the electric field at a point 2.0 cm from the center of the two surfaces?

A) 1.1 N/C
B) 4.5 N/C
C) 1.4 N/C
D) 5.6 N/C
E) 0.50 N/C

Question 58

An uncharged spherical conducting shell surrounds a charge −q at the center of the shell. The charges on the inner and outer surfaces of the shell are respectively

A) −q, −q.
B) −q, +q.
C) +q, −q.
D) +q, +q.
E) +q, 0.

Question 59

Charge of uniform linear density (4.0 nC/m) is distributed along the entire x axis. Determine the magnitude of the electric field on the y axis at y = 2.5 m.

A) 36 N/C
B) 29 N/C
C) 43 N/C
D) 50 N/C
E) 58 N/C

Question 60

A solid nonconducting sphere (radius = 12 cm) has a charge of uniform density (30 nC/m³) distributed throughout its volume. Determine the magnitude of the electric field 15 cm from the center of the sphere.

A) 22 N/C
B) 49 N/C
C) 31 N/C
D) 87 N/C
E) 26 N/C

Question 61

A uniform electric field is present in the region between infinite parallel plane plates A and B and a uniform electric field is present in the region between infinite parallel plane plates B and C. When the plates are vertical, is directed to the right and to the left. The signs of the charges on plates A, B and C may be

A) −, −, −.
B) +, −, −.
C) +, −, +.
D) +, +, +.
E) any one of the above.

Question 62

An uncharged spherical conducting shell surrounds a charge −q at the center of the shell. Then charge +3q is placed on the outside of the shell. When static equilibrium is reached, the charges on the inner and outer surfaces of the shell are respectively

A) +q, −q.
B) −q, +q.
C) +q, +2q.
D) +2q, +q.
E) +3q, 0.

Question 63

Two planes of charge with no thickness, A and B, are parallel and vertical. The electric field in the region between the two planes has magnitude . The electric field in the region to the left of A and the electric field in the region to the right of B may have the magnitudes

A) 0, 0.
B)
,
.
C)
,
.
D) given in any answer above.
E) given only in answer (a) or (b) above.

Question 64

You are told that summed over both the surface areas of sphere A and sphere B below totals to . You can conclude that

A) Sphere A contains charge q_in = −Q.
B) Sphere B contains charge q_in = −Q.
C) Sphere B contains charge q_in = +Q.
D) Each sphere contains charge
.
E) The sum of the charges contained in both spheres is −Q.

Question 65

A spaceship encounters a single plane of charged particles, with the charge per unit area equal to σ. The electric field a short distance above the plane has magnitude ____ and is directed ____ to the plane.

A)
, parallel
B)
, perpendicular
C)
, parallel
D)
, perpendicular
E)
, parallel

Question 66

A constant electric field is present throughout a region of space that includes the plane bounded by the x and y axes and the lines x = 30 cm and y = 50 cm. The electric flux through the plane's surface, in N ⋅ m²/C, is

A) 0.
B) 0.25.
C) 25.
D) 50.
E) 100.

Question 67

A beam of electrons moves at velocity . The number of particles per unit volume in the beam of area A is ρ. If we imagine a cylindrical Gaussian surface of radius r and length centered on the beam, the electron flux through the surface is

A) 0.
B) ρv_fA.
C) 2ρv_fA.
D) ρv_f(A+2πr
).
E) 2ρv_f(A+πr
).

Question 68

Three infinite planes of charge, A, B and C, are vertical and parallel to one another. There is a uniform electric field to the left of plane A and a uniform electric field to the right of plane C. The field points to the left and the field points to the right. The signs of the charges on plates A, B and C may be

A) −, −, −.
B) +, −, −.
C) +, −, +.
D) +, +, +.
E) any one of the above.

Question 69

A constant electric field is present throughout a region of space that includes the plane bounded by the y and z axes and the lines y = 50 cm and z = 50 cm. The electric flux through the plane's surface, in N ⋅ m²/C, is

A) 0.
B) 0.25.
C) 25.
D) 50.
E) 100.

Question 70

If we define the gravitational field , where is a unit radial vector, then Gauss's Law for gravity is

A)
.
B)
.
C)
.
D)
.
E)
.

Question 71

The nucleus of lead-208, , has 82 protons within a sphere of radius 6.34 × 10−¹⁵. Each electric charge has a value of 1.60 × 10−¹⁹ C. Assuming that the protons create a spherically symmetric distribution of charge, calculate the electric field at the surface of the nucleus.

Question 72

Two planes of charge with no thickness, A and B, are parallel and vertical. The electric field in region I to the left of plane A has magnitude and points to the left. The electric field in the region to the right of B has magnitude and points to the right. The electric field in the region between the two planes has magnitude and points to the right. The surface charge density on planes A and B respectively is

A)
, σ.
B)
, σ.
C) σ,
.
D) σ,
.
E) 2σ, σ.

Question 73

A student has made the statement that the electric flux through one half of a Gaussian surface is always equal and opposite to the flux through the other half of the Gaussian surface. This is

A) never true.
B) never false.
C) true whenever enclosed charge is symmetrically located at a center point, or on a center line or centrally placed plane.
D) true whenever no charge is enclosed within the Gaussian surface.
E) true only when no charge is enclosed within the Gaussian surface.

Question 74

A uniform electric field is present in the region between the infinite parallel planes of charge A and B, and a uniform electric field is present in the region between the infinite parallel planes of charge B and C. When the planes are vertical and the fields are both non-zero,

A)
and
are both directed to the right.
B)
and
are both directed to the left.
C)
points to the right and
to the left.
D)
points to the left and
to the right.
E) Any one of the above is possible.

Question 75

A student has made the statement that the electric flux through one half of a Gaussian surface is always equal to the flux through the other half of the Gaussian surface. This is

A) never true.
B) never false.
C) true whenever enclosed charge is symmetrically located at a center point, on a center line, or on a centrally placed plane.
D) true whenever no charge is enclosed within the Gaussian surface.
E) true only when no charge is enclosed within the Gaussian surface.

Question 76

At the point of fission, a nucleus of U-238, with 92 protons is divided into two smaller spheres each with 46 protons and a radius of 5.9 × 10−¹⁵ m. What is the repulsive force pushing the two spheres apart when they are just touching one another? (The mass of the U-238 nucleus is 3.98 × 10−²⁵ kg.)

Question 77

Gino says that the analog of Gauss's law for the flow of an incompressible fluid of density ρ at constant velocity is for an imaginary surface within the fluid. Lorenzo says that it is true only if the area where the fluid enters the surface and the area where it leaves the surface are both perpendicular to the velocity of the fluid. Which one, if either, is correct?

A) Gino, because as much fluid leaves as enters.
B) Lorenzo, because
is not equal to zero if the fluid enters or exits at angles other than 90°.
C) Lorenzo, because this is true only when the fluid executes rotational motion.
D) Gino, because it is true only when the fluid is enclosed on all sides, not when it is flowing.
E) Lorenzo, because it is true only when the fluid is enclosed on all sides, not when it is flowing.

Question 78

Whitney says that Gauss's Law can be used to find the electric field of a sufficiently symmetrical distribution of charge as long as over the whole Gaussian surface. Algie says that the electric field must be a constant vector over the entire Gaussian surface. Which one, if either, is correct?

A) Whitney, because that means no charge is enclosed within the Gaussian surface.
B) Algie, because a constant electric field means that
.
C) Both, because the conditions in (a) and (b) are equivalent.
D) Neither, because the electric field can be found from Gauss's law only if
holds only over a portion of the Gaussian surface.
E) Neither, because the charge distribution must be symmetric if
anywhere on the surface.

Question 79

An constant electric field, N/C, goes through a surface with area m². (This surface can also be expressed as an area of 10 m² with the direction of the unit vector ( ). What is the magnitude of the electric flux through this area?

A) 24 N ⋅ m²/C
B) 48 N ⋅ m²/C
C) 0.24 N ⋅ m²/C
D) 0.48 N ⋅ m²/C
E) 0

Question 80

A point charge is located at the origin. Centered along the x axis is a cylindrical closed surface of radius 10 cm with one end surface located at x = 2 m and the other end surface located at x = 4 m. If the magnitude of the electric flux through the surface at x = 2 m is 4 N ⋅ m²/C, what is the magnitude of the electric flux through the surface at x = 4 m?

A) 1 N ⋅ m²/C
B) 2 N ⋅ m²/C
C) 4 N ⋅ m²/C
D) 16 N ⋅ m²/C
E) The correct value is not given.